TOKYO — South Korea has formally asked to join the 12-nation Trans-Pacific Partnership trade deal, which is finally beginning to make some progress in Congress, but the United States has told it to wait until the pact is agreed on.

With a “fast-track authority” bill about to be introduced in the Senate, the Obama administration is loath to slow the momentum by allowing another country to join the talks — and certainly not one known for its aggressive negotiating stance when it comes to trade deals.

Moon Jae-do, a vice trade minister, and several other key Korean trade officials were greeted with an “unwelcoming atmosphere” when they visited Washington this month, one South Korean trade official said.

They met Wendy Cutler, the acting deputy U.S. trade representative who was the chief American negotiator in the U.S.-Korea free trade deal, and Caroline Atkinson, President Obama’s deputy national security adviser for international economics.

“In principle, the U.S. knows that Korea will have to join TPP at some stage, but they said not right now, they’re busy with the existing countries,” the Korean official said, speaking on the condition of anonymity because he was not authorized to publicly discuss the talks.

The U.S. officials told the Korean visitors that they could join in a second wave once the deal is completed.

“Of course we won’t like it if our choice is take it or leave it,” the Korean official said. “That’s why Korea wants to join as soon as possible, before the negotiations are finished.”

TPP has faced significant resistance in Congress — with some opponents holding up the U.S.-Korea bilateral trade pact as proof that such deals do not work out well for America.

Now, a bill to be introduced in the Senate would give the administration fast-track authority, officially known as “trade promotion authority,” or TPA. That would give negotiators parameters for a deal that would then face only an up-or-down vote in Congress and would not be subject to amendments.

Senate leaders are hoping to schedule a vote on TPA late in the summer but before the presidential campaigns get in full swing, according to people briefed on the timetable.

The Office of the U.S. Trade Representative welcomed Korea’s interest in the trade deal, said Trevor Kincaid, a spokesman, adding that Cutler and Moon had “a productive discussion” during the recent visit.

An administration official said that Moon’s meeting with Atkinson was “warm and friendly and constructive.”

Still, it was clear that the administration sees no room for extra parties at this stage.

“We are currently focused on concluding a high-standard TPP with the current members,” Kincaid said.

The U.S. resistance is “completely understandable,” said Edward Alden, a trade expert at the Council on Foreign Relations.

“It would complicate the domestic politics, right on the eve of the fast-track authority debate,” he said. “The president needs this TPA vote, but he already has minimal support for this in his own party, and Korea will only make it worse.”

The pact would establish the world’s largest free-trade zone, incorporating 12 Asia-Pacific countries that include the United States and Japan, and would cut tariffs, establish guidelines on patents and copyrights, and level competition for international companies that compete with government-backed businesses.